Academic literature on the topic 'Ultimately periodic infinite'
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Journal articles on the topic "Ultimately periodic infinite"
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Costa, José Carlos, Conceição Nogueira, and Maria Lurdes Teixeira. "The Overlap Gap Between Left-Infinite and Right-Infinite Words." International Journal of Foundations of Computer Science 33, no. 01 (2021): 45–53. http://dx.doi.org/10.1142/s0129054121500350.
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We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word [Formula: see text] and the prefixes of a right-infinite word [Formula: see text]. The main theorem states that the set of minimum lengths of words [Formula: see text] and [Formula: see text] such that [Formula: see text] or [Formula: see text] is finite, where [Formula: see text] runs over positive integers and [Formula: see text] and [Formula: see text] are respectively the suffix of [Formula: see text] and the prefix of [Formula: see text] of length [Formula: see text], if and only if [Formula: see text] and [Formula: see text] are ultimately periodic words of the form [Formula: see text] and [Formula: see text] for some finite words [Formula: see text], [Formula: see text] and [Formula: see text].
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Marcus, Solomon. "Bridging Two Hierarchies of Infinite Words." JUCS - Journal of Universal Computer Science 8, no. (2) (2002): 292–96. https://doi.org/10.3217/jucs-008-02-0292.
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Infinite words on a finite non-empty alphabet have been investigated in various respects. We will consider here two important strategies in approaching such words; one of them proceeds from particular to general, while the other proceeds from general to particular. As we shall see, the respective hierarchies don't interfer. There is between them an empty space waiting for investigation. 1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen.
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BELL, JASON, EMILIE CHARLIER, AVIEZRI S. FRAENKEL, and MICHEL RIGO. "A DECISION PROBLEM FOR ULTIMATELY PERIODIC SETS IN NONSTANDARD NUMERATION SYSTEMS." International Journal of Algebra and Computation 19, no. 06 (2009): 809–39. http://dx.doi.org/10.1142/s0218196709005330.
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Consider a nonstandard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language.
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Bucci, Michelangelo, and Gwenaël Richomme. "Greedy Palindromic Lengths." International Journal of Foundations of Computer Science 29, no. 03 (2018): 331–56. http://dx.doi.org/10.1142/s0129054118500077.
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In [A. Frid, S. Puzynina and L. Q. Zamboni, On palindromic factorization of words, Adv. in Appl. Math. 50 (2013) 737–748], it was conjectured that any infinite word whose palindromic lengths of factors are bounded is ultimately periodic. We introduce variants of this conjecture and prove this conjecture when the bound is 2. Especially we introduce left and right greedy palindromic lengths. These lengths are always greater than or equals to the initial palindromic length. When the greedy left (or right) palindromic lengths of prefixes of a word are bounded then this word is ultimately periodic.
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Yang, Ping, Xu Wang, and Peter Schiavone. "Elastic cloaking for a periodic distribution of parallel finite cracks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2249 (2021): 20200997. http://dx.doi.org/10.1098/rspa.2020.0997.
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We achieve elastic cloaking for a periodic distribution of an infinite number of parallel finite mode III cracks by means of the complex variable method and the theory of Cauchy singular integral equations. The cloaking bimaterial structure is composed of an undisturbed uniformly stressed left half-plane perfectly bonded via a wavy interface to the right half-plane which contains periodic cracks. The original design of the wavy interface and the positions of the periodic cracks are ultimately reduced to the solution of a Cauchy singular integral equation which can be solved numerically.
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D'Angeli, Daniele, Dominik Francoeur, Emanuele Rodaro, and Jan Philipp Wächter. "On the orbits of automaton semigroups and groups." Algebra and Discrete Mathematics 33, no. 1 (2022): 1–29. http://dx.doi.org/10.12958/adm1692.
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We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivalent to the finiteness problem for left principal ideals in automaton semigroups generated by complete and reversible automata. Then, we look at w-word (i.\,e.\ right infinite words) with a finite orbit. We show that every automaton yielding an w-word with a finite orbit already yields an ultimately periodic one, which is not periodic in general, however. On the algorithmic side, we observe that it is not possible to decide whether a given periodic w-word has an infinite orbit and that we cannot check whether a given reversible and complete automaton admits an w-word with a finite orbit, a reciprocal problem to the finiteness problem for automaton semigroups in the reversible case. Finally, we look at automaton groups generated by reversible but not bi-reversible automata and show that many words have infinite orbits under the action of such automata.
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MATSUMOTO, KENGO, and HIROKI MATUI. "TOPOLOGICAL FULL GROUPS OF -ALGEBRAS ARISING FROM -EXPANSIONS." Journal of the Australian Mathematical Society 97, no. 2 (2014): 257–87. http://dx.doi.org/10.1017/s1446788714000214.
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AbstractWe introduce a family of infinite nonamenable discrete groups as an interpolation of the Higman–Thompson groups by using the topological full groups of the groupoids defined by $\beta $-expansions of real numbers. They are regarded as full groups of certain interpolated Cuntz algebras, and realized as groups of piecewise-linear functions on the unit interval in the real line if the $\beta $-expansion of $1$ is finite or ultimately periodic. We also classify them by a number-theoretical property of $\beta $.
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KARWEIT, MICHAEL, and PHILIPPE BLANC-BENON. "TEMPORAL CHARACTERISTICS OF ACOUSTIC RAY PROPAGATION THROUGH "INFINITE" AND "BOX MODEL" TURBULENCE." Journal of Computational Acoustics 03, no. 03 (1995): 203–18. http://dx.doi.org/10.1142/s0218396x95000094.
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In this work, we investigate the temporal characteristics of acoustic ray propagation through simulated, weakly turbulent temperature fields. In a first set of experiments, we generate ensembles of random scalar fields from randomly oriented Fourier temperature modes. Then, by integrating the ray trace equations, we estimate the distribution of arrival times for rays propagating a distance R through them. We demonstrate that these arrival time distributions are Gaussian for both axial and 3-D propagation and are primarily determined by the lower wave numbers of the 1-D fluctuation spectrum. In a second set of experiments, we generate random fields comprised of Fourier modes prescribed on a lattice, as in "box model" turbulence. In these simulations, we find that acoustic travel times are significantly affected both by the periodicity of the fields and by the direction of acoustic propagation with respect to the orientation of the box. Both effects can ultimately be attributable to an inadequate representation of the low wave number region of the 1-D spectrum. We suggest that these artifacts of simulated periodic fields may preclude their use for acoustic propagation studies.
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ILIE, LUCIAN, SHENG YU, and KAIZHONG ZHANG. "WORD COMPLEXITY AND REPETITIONS IN WORDS." International Journal of Foundations of Computer Science 15, no. 01 (2004): 41–55. http://dx.doi.org/10.1142/s0129054104002297.
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With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R (w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB , and Lempel-Ziv complexity, LZ . We have always R (w)≥ LZ (w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) [Formula: see text], (ii) [Formula: see text], and (iii) [Formula: see text]. De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R (w) can be computed in time [Formula: see text] and it is open, and probably very difficult, to find fast algorithms.
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ZANTEMA, HANS. "TURTLE GRAPHICS OF MORPHIC SEQUENCES." Fractals 24, no. 01 (2016): 1650009. http://dx.doi.org/10.1142/s0218348x16500092.
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The simplest infinite sequences that are not ultimately periodic are pure morphic sequences: fixed points of particular morphisms mapping single symbols to strings of symbols. A basic way to visualize a sequence is by a turtle curve: for every alphabet symbol fix an angle, and then consecutively for all sequence elements draw a unit segment and turn the drawing direction by the corresponding angle. This paper investigates turtle curves of pure morphic sequences. In particular, criteria are given for turtle curves being finite (consisting of finitely many segments), and for being fractal or self-similar: it contains an up-scaled copy of itself. Also space-filling turtle curves are considered, and a turtle curve that is dense in the plane. As a particular result we give an exact relationship between the Koch curve and a turtle curve for the Thue–Morse sequence, where until now for such a result only approximations were known.
Book chapters on the topic "Ultimately periodic infinite"
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Doveri, Kyveli, Pierre Ganty, and Luka Hadži-Đokić. "Antichains Algorithms for the Inclusion Problem Between $$\omega $$-VPL." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_15.
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AbstractWe define novel algorithms for the inclusion problem between two visibly pushdown languages of infinite words, an EXPTime-complete problem. Our algorithms search for counterexamples to inclusion in the form of ultimately periodic words i.e. words of the form $$uv^{\omega }$$ u v ω where $$u$$ u and $$v$$ v are finite words. They are parameterized by a pair of quasiorders telling which ultimately periodic words need not be tested as counterexamples to inclusion without compromising completeness. The pair of quasiorders enables distinct reasoning for prefixes and periods of ultimately periodic words thereby allowing to discard even more words compared to using the same quasiorder for both. We put forward two families of quasiorders: the state-based quasiorders based on automata and the syntactic quasiorders based on languages. We also implemented our algorithm and conducted an empirical evaluation on benchmarks from software verification.
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Webster, Erin. "Perspective as a Conceptual Tool in Milton and Newton." In The Curious Eye. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198850199.003.0006.
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This chapter reads John Milton’s use of vast shifts in perspective in Paradise Lost (1667) in relation to seventeenth-century developments in the mathematics of infinity and infinitesimals. In a period in which telescopes and microscopes promised to extend the eye’s reach indefinitely, this chapter shows that Milton’s use of the epic simile and Newton’s infinitesimal calculus, first published as an attachment to his optical treatise, Opticks (1704), are related attempts to express concepts that continue to exceed the limits of visual comprehension: the infinitely large, the infinitesimally small, and the paradoxical relationship between the two. The chapter places these two writers’ work within the context of baroque art and architecture, which similarly exploits perspective as a means of expressing the concept of an infinite universe held in tension with the limits of human perception. Ultimately, it argues that by requiring his readers to vacillate between multiple perspectives on the same object, Milton contributes to a broader cultural decentring of the earth-bound human perspective as the standard measure of the universe.
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Reutenauer, Christophe. "Basics." In From Christoffel Words to Markoff Numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0002.
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Definitions and basic results about words: alphabet, length, free monoid, concatenation, prefix, suffix, factor, conjugation, reversal, palindrome, commutative image, periodicity, ultimate periodicity, periodic pattern, infinite words, bi-infinite words, free groups, reduced words, homomorphisms, embedding of a free monoid in a free group, abelianization,matrix of an endomorphism, GL<sub>2</sub>(Z), SL<sub>2</sub>(Z).
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Springborg, Michael, and Bernard Kirtman. "Electronic orbital responses of extended systems to static, homogeneous, electromagnetic fields." In Chemical Modelling. Royal Society of Chemistry, 2024. https://doi.org/10.1039/9781837672554-00018.
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We discuss theoretical methods with which the effects of static, homogenous, electromagnetic fields can be determined for systems that are extended and in the ultimate limit are infinite and periodic. We focus here on the finite field (FF) method, but there are obvious implications for perturbation theory approaches as well. The fact that including finite fields in electronic-structure calculations simultaneously introduces the coordinate r→ means that the translational invariance of the potential would be violated and therefore without modification this approach would be inapplicable to infinite, periodic systems. One such long-standing approach is to replace r→ by an operator that involves the derivative with respect to the crystal momentum k→. This is the primary procedure for electrostatic fields. For magnetostatic fields a number of suggestions have been made, all of which are or may be related to changing the gauge used to describe the fields. In the case of a large finite system, for non-vanishing electrostatic and/or magnetostatic field, the lowest energy orbitals are unbound. Thus, the bound states become resonances and the bound-state variational principle can no longer be applied. Instead, special methods for identifying the changes in the system properties due to the presence of these fields are evaluated. Our own simple method based on identifying those orbitals in the field-containing case that are most similar to the occupied orbitals in the field-free case seems to be a promising approach. Since methods for finite molecular systems exposed to static electromagnetic fields are more mature than those for the infinite, periodic crystals, an important issue is to establish that these methods give identical results when treating a crystal as being either large and finite or infinite and periodic. Finally it shall be mentioned that our presentation focuses on methods rather than results. Moreover, it concentrates on our own work that, in some cases, is not yet complete.
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"Helena Blavatsky: The Secret Doctrine 1888." In Milestone Documents of World Religions. Schlager Group Inc., 2011. https://doi.org/10.3735/9781935306191.book-part-081.
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The Secret Doctrine is the magnum opus of Helena Blavatsky. In it, Blavatsky lays out the fundamental basis for Theosophy, a religious philosophy that she believed to be an ageless, universal system for understanding how the earth came to be and humanity's connection to the unseen divine. She drew upon a number of disparate sources to craft her system, including Hindu reincarnation and Darwinian evolution. At its base, Theosophy teaches that everything—the human soul, the earth, the solar system—is proceeding through a set of seven reincarnation periods. The periods can be thought of as one infinitely long breath emanating from the Ultimate Truth. During the outbreath (expansion), everything cycles away from spiritual Oneness, culminating in the fourth period, when we are farthest away and thus visible in material form. After this apex, we begin the journey back, returning to the ultimate goal of all material forms: spiritual Oneness and Truth.
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Mitchell, A. Wess. "Epilogue." In The Grand Strategy of the Habsburg Empire. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691196442.003.0011.
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This epilogue argues that many of the problems that the Habsburgs faced are present today. Geopolitics remains as a persistent and reintensifying force in which Great Powers seek to survive in competition with other large, purposeful actors. In this contest, geography remains both a key determinant of success and its ultimate prize. Advances in technology have only partially mitigated the effects of geography; even in the era of nuclear weapons, the search for security comes down to a battle for space in which finite resources must be arrayed in time to deal with virtually infinite challenges. As in the Habsburg period, the threats arrayed against today’s West are multidirectional in nature and vary widely in form, ranging from revisionist Great Powers with large conventional armies to economically backward but numerous and religiously motivated enemies employing asymmetrical weapons and tactics. The chapter then considers a few broad principles of Habsburg strategic statecraft which stand out as potentially relevant in any era.
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Lee, John A. L. "Auxiliary θє́λω." In The Language of the Papyri. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780199237081.003.0002.
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Abstract The future tense in Modern Greek is formed with Łæ subjunctive, as for example, θɑϒρɑˊϕω. This form of expression has its origin in a periphrasis with θє́λω. The ultimate base is θє́λω infinitive, with θє́λω in its original meaning ‘wish to ’, which evolves into an expression of simple futurity. The development is parallel to that in many languages, among them of course English, in which futurity is expressed by an auxiliary that originally meant ‘wish/want ‘; or to put it in terms of grammaticalization, the lexical item ‘wish/want ‘ has evolved along the cline of grammaticality to a grammatical function, namely, to express futurity. The detailed history of the development in the Byzantine period is not the concern of this paper and will be touched on only briefy. It is more complicated than one might have expected, and debate continues on the details.
Conference papers on the topic "Ultimately periodic infinite"
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Liang, Yang, and B. F. Feeny. "Parametric Identification of Chaotic Systems Via a Long-Period Harmonic Balance." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85032.
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Hyperbolic chaotic sets are composed of a countable infinity of unstable periodic orbits (UPOs). Symbol dynamics reveals that any long chaotic segment can be approximated by a UPO, which is a periodic solution to an ideal model of the system. Treated as such, the harmonic balance method is applied to the long chaotic segments to identify model parameters. Ultimately, this becomes a frequency domain identification method applied to chaotic systems.
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Bhide, Sarang, Priyank Srivastava, Rajesh Jain, and Rajesh Fife. "Production Data Diagnostics based on Inflow Performance Relationship of pumping wells in CBM Fields." In Gas & Oil Technology Showcase and Conference. SPE, 2023. http://dx.doi.org/10.2118/214273-ms.
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Abstract Coal Bed Methane (CBM) is a type of unconventional resource wherein methane gas adsorbed on surface of coal seams is produced by dewatering waterfilled coal seams and thereby causing desorption of the gas. This paper aims at applying quick look diagnostic curves to assess performance of Coal Bed Methane (CBM) wells which traditionally encounter high frequency workovers with reservoir heterogeneity and complex physics. Currently, very few production diagnostic tools are available to access / predict unconventional Coal Bed Methane (CBM) well behavior. Use of production diagnostic curves using pressure-rate data is presented to distinguish the well performance with variety of completion types and artificial lift strategies which provides gainful insights into relative well performance. Inferences could be used to plan / optimize for future development strategies for infill drilling. Response based diagnostic tools are derived using P-Q (Pressure-Rate) and PI-Cum. (Productivity Index - Cum. Prod.) plots and extrapolation of trends can be used to guesstimate the expected ultimate recoveries and drainage area for CBM wells. Thus, typical characteristics of these performance plot gives clear indication of qualitative desorption front. Diagnostic P-Q and PI-Cum. performance curves were generated for various on-stream CBM wells and these curves were used to identify and predict the flow regime in wells with different completion scenarios. Single phase Inflow-Performance Relationship (IPR) shows a typical behavior in most of the wells and analysis of life-cycle IPR indicates a characteristic signature for on-set of pseudo-steady state (PSS). Flow regimes which can be clearly identified are initial flow i.e. Infinite acting radial flow (IARF), completion/intervention dependent flow and PSS flow. The initial flow period involves dewatering of coal seam and hence generates a hyperbolic curve on the p-q plot. As desorption front advances further, peak gas production is observed and this phase can be prolonged by effective use of Artificial lift (AL) strategies to maximize the drawdown. The well soon shows positive slope line on IPR that corresponds to Pseudo-steady state or Boundary dominated flow. At this juncture the drainage boundary of the well is properly defined and so is the Expected Ultimate Recovery (EUR). This phase is the longest in terms of well life cycle. These diagnostic tools were highly useful in well and reservoir performance analysis to optimize the AL and workover practices for CBM wells. This paper brings out novel approach towards analysis of production data from CBM field with wells operating on Progressive Cavity Pumps (PCP's) to dewater coal beds, it brings out a way to qualitatively estimate the desorption front and quantitatively deduce the EUR’s of the wells. This paper proposes a way to generate "Type well" analysis for CBM field and augment a reliable production forecasting.
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Stankowski, Alexander. "Advanced Thermochemical Cleaning Procedures for Structural Braze Repair Techniques." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30535.
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Hot gas path components of modern Industrial Gas Turbines (IGT) are exposed to extreme thermal, mechanical and chemical loading that ultimately leads to their deterioration. Modern GT designs provide for safe operation for a certain operation period. Higher firing temperatures and changing machine loads as a result of the deregulated markets call for highly sophisticated part designs and the use of cost-intensive superalloys. As the lifetime of critical parts is not infinite, they are reconditioned periodically or replaced to regain efficiency losses and to mitigate the risk of unscheduled outages due to hot gas path (HGP) failures. This paper presents advanced thermochemical preparation treatments that form the basis for the subsequent structural repairs, such as high temperature brazing. Before executing any repair step, coated components must be stripped of the consumed and degenerated coatings. Not all of the many techniques that are commonly used can guarantee reproducible and complete removal without damaging the substrate. Recently improved thermochemical techniques, such as a combination of advanced Chemical Stripping and Salt Bath Cleaning, enables the OEM to obtain clean components at low unit costs and for short processing times. In previous approaches, CrF2- and PTFE-based processes were used to clean surfaces and, principally, cracks from oxide scales before welding or brazing was carried out. These preparation techniques were indispensable for reworking superalloys, which cannot be cleaned sufficiently using conventional methods such as exposure under reducing atmospheres at high temperatures. Today, the high versatility of the “Dynamic Subatmospheric Fluoride Ion Cleaning” process (FIC) enables the OEM to run precisely tailored processes, allowing complete freedom to adjust the chemical activity of the gas phase and in so doing fulfil the specific conditions for any superalloy being reworked, even taking into account the varying grade of degradation sustained during service exposure. Weld repairs on superalloys are very sensitive to hot cracking, and high temperature brazing has established itself as a successful method for overcoming this problem. Furthermore, the intensively FIC cleaned surfaces can be regarded as the most important condition to enable a high quality bonding. Other key advantages of braze repairs are the uniform heat input that is possible, the high shape tolerance and the fact that multiple cracks can be simultaneously repaired. In addition, the brazing heat treatment allows controlled adjustment of the microstructural properties. Besides the economic benefits of the treatment, the brazed parts show excellent results in respect of their mechanical integrity. A schematic presentation of the repair sequence described in this paper is shown in the appendix (Fig. 17).